Problem: $\dfrac{ -5j - 8k }{ 3 } = \dfrac{ 7j - l }{ -9 }$ Solve for $j$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -5j - 8k }{ {3} } = \dfrac{ 7j - l }{ -9 }$ ${3} \cdot \dfrac{ -5j - 8k }{ {3} } = {3} \cdot \dfrac{ 7j - l }{ -9 }$ $-5j - 8k = {3} \cdot \dfrac { 7j - l }{ -9 }$ Multiply both sides by the right denominator. $-5j - 8k = 3 \cdot \dfrac{ 7j - l }{ -{9} }$ $-{9} \cdot \left( -5j - 8k \right) = -{9} \cdot 3 \cdot \dfrac{ 7j - l }{ -{9} }$ $-{9} \cdot \left( -5j - 8k \right) = 3 \cdot \left( 7j - l \right)$ Distribute both sides $-{9} \cdot \left( -5j - 8k \right) = {3} \cdot \left( 7j - l \right)$ ${45}j + {72}k = {21}j - {3}l$ Combine $j$ terms on the left. ${45j} + 72k = {21j} - 3l$ ${24j} + 72k = -3l$ Move the $k$ term to the right. $24j + {72k} = -3l$ $24j = -3l - {72k}$ Isolate $j$ by dividing both sides by its coefficient. ${24}j = -3l - 72k$ $j = \dfrac{ -3l - 72k }{ {24} }$ All of these terms are divisible by $3$ $j = \dfrac{ -{1}l - {24}k }{ {8} }$